## Açık İşletmelerde Optimum Üretim Planlamasında Yeni Bir Yöntem Geliştirilmesi

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2015-07-10
Özkan, Murat
##### Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science And Technology
##### Özet
Open pit mine production planning is an optimization process involving many parameters from the beginning of mine life to end of mine life. Main idea behind the open pit production planning is the maximization of net present value or maximization of the total profit considering physical and economical constraints. When maximizing the net present value, determining ultimate open pit limit and production scheduling are decisive parameters. Finding ultimate pit limit is finding optimum boundaries of an open pit that maximizes the total profit. However, this procedure maximizes the undiscounted profit. The time value of the money is not considered. The best and the most reliable methods to find the ultimate pit limit is Lerchs and Grossmann algorithm and maximum flow algorithm as everyone agrees. On the other hand, Moving Cone or Floating Cone algorithm is fast, simple, easy to understand and program therefore is used in many integrated mine design and planning software because of these reasons. Open pit production scheduling or block scheduling are the problem of when to excavate which ore or waste block. When optimizing production scheduling net present value (NPV) from the pit should be maximized by considering the time value of money (discount rate). This means that profit obtained from pit at any time should be discounted. One reason this should be done, because the economical parameters such as mineral prices and costs can change in time. Another reason mine operator wants to recover capital cost invested at the beginning of the mine as early as possible. Many methods are developed in order to find the optimum open pit production schedule from 1960s to the present year like Linear Programming (LP), Integer Programming (IP), Mixed Integer Programming (MILP), Dynamic Programming (DP), Genetic Algorithms, Artificial Intelligence and Heuristic methods. The most commonly used method among these is to find nested pits by using parameterization technique. This technique is used by many mining software and can be applied changing input parameters like Revenue Adjustment Factor (RAF) and find a series of nested pits in every change. There are many researchers and researches on open pit mine production planning optimization. Many of these researches first find ultimate open pit limit then tries to schedule production considering pit limits. However, when finding ultimate pit limit, time value of blocks are not considered and assumed they all have present values it remains the question of the ultimate pit limit is optimum or not. Because of this reason many researchers tried to develop methods that optimize the production planning and the ultimate pit limit simultaneously. In these methods, it is known which block is excavated when therefore it is possible to assign economical values to the blocks considering time factor. In this doctoral research, previous researches tries to optimize long term production planning in open pit mines are examined and an alternative algorithm for open pit mine planning is developed. It is claimed that new algorithm developed works better than previous algorithms. The new algorithm optimizes open pit scheduling problem and finds the ultimate pit limit simultaneously by considering the time value of money. The algorithm gives higher total profit or net present value (NPV) than any other methods. In the algorithm developed, the net present value (NPV) is maximized by using the variables determine the net present value (NPV) of the blocks instead of using a constant net present value (NPV) of the blocks. In order to that, unit profit is maximized by considering the variables such as block economical values and production rate. The aim is to maximize block economic value per extracted unit volume. In other words, the best sequence to maximize net present value (NPV) is to maximize block economic value per block (BEVPB). To find these BEVPBs the moving cone algorithm is utilized. The algorithm developed is called “Improved Moving Cone” algorithm. Improved moving cone algorithm works on block with economical values. In every iteration, block clusters not exceeding yearly production rate and with maximum economical value per cubic meter are found and deleted from the block model. When searching for the block clusters positive cone is used. When a positive block cluster is found these blocks are deleted from the model after they are optimized with negative cone (Reverse Cone). This step is repeated until no block with positive or zero value is remained. When there is no block cluster remains it means that ultimate pit limit is reached. After every iteration, block clusters are grouped according to yearly production amount and then net present value is calculated for every production rate in the block model. In order to test and compare developed improved moving cone algorithm with other previously developed ultimate pit limit and production planning algorithms, a 2D example problem is developed. The results obtained are compared with Lerchs and Grossmann (1965) algorithm and parameterization method developed by Wang and Sevim (1992). When the results are compared, it has been seen that the results were promising. The algorithm gives the same results with Lerchs and Grossmann algorithm for determining ultimate open pit limit and better results than Wang and Sevim’s suggestion for maximizing net present value (NPV). Because of the promising results, a program is developed for 3D problems by using MS Visual Basic programming language. For 3D problem, a magnetite ore deposit is chosen as sample study area. The drillhole logs and topographic map is reorganized and used for example study. After that block model for ore and waste is developed in Micromine software. Block model has 279.658 blocks. On this block model, first ultimate pit is found by using Lerchs and Grossman algorithm, and then nested pits are obtained by parameterization method. Production planning is achieved by using Improved Moving Cone Algorithm. After examining the results, it is concluded that Improved Moving Cone Algorithm gives the same optimum results with Lerchs and Grossman algorithm. There are 104.166.000 tons of ore and 144.504.000 tons of waste in the optimum pit limits. Stripping ratio was found 1,39 ton/ton. Revenue was 1.380.800.860TL as undiscounted cash. When it comes to production scheduling, Improved Moving Cone Algorithm gives higher net present value (934.557.426TL) than The Best Case Scenario (928.238.520TL) in nested pit parameterization method if the discount rate is %10. In addition, annual production targets are better achieved than nested pits. The algorithm does not gives gap problem. As a results, developed Improved Moving Cone Algorithm, optimizes ultimate open pit limit and production scheduling problems simultaneously and results in higher net present value. Therefore, it is a better alternative to previously developed algorithms. In the future, it can be possible to apply easily different slope angles or some important constraints like annual production rate to the algorithm.
##### Açıklama
Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2015
Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2015
##### Anahtar kelimeler
Açık Ocak İşletmeciliği, Madenlerde Üretim Planlaması, Optimizasyon, Open Pit Mining, Mine Production Planning, Optimization